Typical automorphism groups of finite nonrigid structures

Vera Koponen

paper

Typical automorphism groups of finite nonrigid structures

arXiv:1310.6973

Abstract

We work with a finite relational vocabulary with at least one relation symbol with arity at least 2. Fix any integer $m > 1$ . For almost all finite structures (labelled or unlabelled) such that at least $m$ elements are moved by some automorphisms, the automorphism group is $(Z_{2})^{i}$ for some $i \leq (m + 1) /2$ ; and if some relation symbol has arity at least 3, then the automorphism group is almost always $Z_{2}$ .

arXiv admin note: substantial text overlap with arXiv:1305.3097